Simultaneous equations with two or more than two variables, Mathematics

Method to solve Simultaneous Equations with two or more than two variables


Above we have seen equations wherein we are required to find the value of the variable x only. Apart from the equations of the type we have seen above, simple equations of the form 7x + 2y = 47 also exists. As against the equations x - 3 = 12 or 3x + 5 = 20 where we had a single variable x, we have two variables x and y. If we express this equation in terms of y it will be

                   7x + 2y                = 47

                   7x - 7x + 2y          = 47 - 7x

                   0 + 2y                  = 47 - 7x

                    2y                      = 47 - 7x

               1407_simultaneous equation.png

In this expression by giving values to x and solving the expression we get corresponding values for y.

Now if another equation of the form 5x - 4y = 1 is expressed in terms of y, we have


= 593_simultaneous equation1.png

For this equation also if we substitute values for x, we would get corresponding values for y.

At this stage if we want values which satisfy both the equations then the values of y in both these equations should be identical. That is,

2040_simultaneous equation2.png

On cross multiplying, we have 4(47 - 7x) = 2(5x - 1)

                   188 - 28x = 10x - 2

Collecting all x terms and constants, we have

                 -10x - 28x    =    - 2 - 188

                         -38x    =    - 190

                              x    =       5

We substitute this value of x = 5, in either of equations to get the value of y.

                   5x - 4y     =     1

                   5(5) - 4y  =     1

                   - 4y         =     1 - 25

                   - 4y         =       - 24

                       y         =       -24/ - 4 = 6.

Therefore, the common values of x and y which satisfy these two equations simultaneously are x = 5 and y = 6. Therefore, we can define simultaneous equations as two or more equations which are satisfied by the same values of x and y (unknown quantities). 

Posted Date: 9/13/2012 3:53:25 AM | Location : United States

Related Discussions:- Simultaneous equations with two or more than two variables, Assignment Help, Ask Question on Simultaneous equations with two or more than two variables, Get Answer, Expert's Help, Simultaneous equations with two or more than two variables Discussions

Write discussion on Simultaneous equations with two or more than two variables
Your posts are moderated
Related Questions
Determine an actual explicit solution to y′ = t/y; y(2) = -1. Solution : We already identify by the previous illustration that an implicit solution to this IVP is y 2 = t 2 -

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equ

1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Perform the denoted operation.                    (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus

1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).

Proof of Constant Times a Function: (cf(x))′ = cf ′(x) It is very easy property to prove using the definition given you a recall, we can factor a constant out of a limit. No

Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5. Ans:    103, 108..........998   a + (n-1)d = 998

Coming To Grips With Mathematics :  How does a child acquire mathematical concepts? Can any concept be presented to a child at any stage in such a manner that the child gets some

For queries Q 1 and Q 2 , we say Q 1 is contained in Q 2 , denoted Q 1 ⊆ Q 2 , iff Q 1 (D) ⊆ Q 2 (D) for every database D. The container problem for a fixed Query Q 0 i

1.A manufacturing facility consists of five departments, 1, 2, 3, 4 and 5. It produces four components having the manufacturing product routings and production volumes indicated in